论文标题
从超材料准颗粒的时间域弹性散射的模态近似
Modal approximation for time-domain elastic scattering from metamaterial quasiparticles
论文作者
论文摘要
本文旨在定量理解时间域中宽带信号下的负超材料结构引起的弹性波散射。具体而言，我们为弹性动力学中的超材料准粒子分散的时间依赖性场建立了模态膨胀。通过傅立叶变换，我们首先分析了时间谐波制度中的模态扩展。在存在准颗粒的情况下，我们通过定量分析与弹性静态系统相关的Neumann-Poincaré运算符的光谱特性来验证静态状态中的这种扩展。然后，我们使用有限数量的模式近似入射场，并应用扰动理论以在扰动状态中获得这种扩展。此外，我们将极化共振作为具有非零频率的弹性系统的简单极点。最后，我们表明，通过使用具有急剧误差估计的谐振模态扩展，可以很好地近似时间域中的散射场的低频部分。
This paper aims at quantitatively understanding the elastic wave scattering due to negative metamaterial structures under wide-band signals in the time domain. Specifically, we establish the modal expansion for the time-dependent field scattered by metamaterial quasiparticles in elastodynamics. By Fourier transform, we first analyze the modal expansion in the time-harmonic regime. With the presence of quasiparticles, we validate such an expansion in the static regime via quantitatively analyzing the spectral properties of the Neumann-Poincaré operator associated with the elastostatic system. We then approximate the incident field with a finite number of modes and apply perturbation theory to obtain such an expansion in the perturbative regime. In addition, we give polariton resonances as simple poles for the elastic system with non-zero frequency. Finally, we show that the low-frequency part of the scattered field in the time domain can be well approximated by using the resonant modal expansion with sharp error estimates.
